The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1
 0  X  0  0  0  0  0  X  X X^2+X X^2 X^2
 0  0  X  0  0  0  X  0  X  X X^2  0
 0  0  0  X  0  X  X  X  0  X X^2+X  0
 0  0  0  0  X  X  0 X^2  0 X^2  0  X
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+53x^6+80x^7+194x^8+272x^9+496x^10+1696x^11+2624x^12+1696x^13+450x^14+272x^15+245x^16+80x^17+24x^18+8x^20+1x^22

The gray image is a linear code over GF(2) with n=48, k=13 and d=12.
This code was found by Heurico 1.16 in 0.134 seconds.